Data compression is a general process of transforming a body of data to a smaller representation from which the original or some approximation to the original can be reconstructed. This process is called lossless compression if the original can be reconstructed; otherwise, it is called lossy compression of information. Although lossless data compression can be applied to any type of data, in practice, it is most appropriate for textual data, where it is typically important to preserve the original data. By contrast, lossy compression is most useful for digitized data such as voice, image, video, where some information may be lost since only the perceived quality of the reconstructed data is important. We study theory, methods and algorithms for lossy data compression in computer networks. This work is focused on algorithms design, bounds and performance analysis, mostly from the point of view of information theory.